后乘，左手坐标系

Originally posted:

矩阵中的轴

[X-AxisY-AxisZ-AxisTranslate↓↓↓↓m11m12m13m14m21m22m23m24m31m32m33m34m41m42m43m44]\begin{array}{c} \begin{bmatrix} \color{red} \textrm{X-Axis} & \color{green} \textrm{Y-Axis} & \color{blue} \textrm{Z-Axis} & \textrm{Translate} \\ \color{red} \downarrow & \color{green} \downarrow & \color{blue} \downarrow & \downarrow \\ \color{red} \mathbf{m_{11}} & \color{green} \mathbf{m_{12}} & \color{blue} \mathbf{m_{13}} & \mathbf{m_{14}}\\ \color{red} \mathbf{m_{21}} & \color{green} \mathbf{m_{22}} & \color{blue} \mathbf{m_{23}} & \mathbf{m_{24}}\\ \color{red} \mathbf{m_{31}} & \color{green} \mathbf{m_{32}} & \color{blue} \mathbf{m_{33}} & \mathbf{m_{34}}\\ \color{gray} m_{41} & \color{gray} m_{42} & \color{gray} m_{43} & \color{gray} m_{44}\\ \end{bmatrix} \end{array}

平移变换

[100Tx010Ty001Tz0001]\begin{bmatrix} 1 & 0 & 0 & T_x\\ 0 & 1 & 0 & T_y\\ 0 & 0 & 1 & T_z\\ 0 & 0 & 0 & 1\\ \end{bmatrix}

反射变换

  • 轴平面对称
XY PlaneXZ PlaneYZ Plane[1000010000−100001][10000−10000100001][−1000010000100001]\begin{array}{ccc} \textrm{XY Plane} & \textrm{XZ Plane} & \textrm{YZ Plane} \\ \begin{bmatrix} 1 & 0 & 0 & 0\\ 0 & 1 & 0 & 0\\ 0 & 0 & -1 & 0\\ 0 & 0 & 0 & 1\\ \end{bmatrix} & \begin{bmatrix} 1 & 0 & 0 & 0\\ 0 & -1 & 0 & 0\\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1\\ \end{bmatrix} & \begin{bmatrix} -1 & 0 & 0 & 0\\ 0 & 1 & 0 & 0\\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1\\ \end{bmatrix} \end{array}

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